A US man who shot and killed a woman who he said was pregnant also claims she and her accomplice had stolen from him before.

Police were still deciding whether to charge Tom Greer, 80, who said he had acted in self-defence and that the pair were the same people who'd twice robbed him before.

"They've been here twice so they know the routine," he told local news station KNBC.

Greer said that he walked into his Long Beach home on Tuesday night to find a man and woman trying to access his safe.

They tackled him, Greer said, but then let him climb to his feet and watch. He said he broke his collar bone in the initial confrontation.

The man then went to the home's garage to find something to help him break into the safe, and while the woman was momentarily distracted, Greer grabbed his gun, a 22-caliber Smith Wesson revolver.

When the couple saw that Greer had armed himself, they ran, he said, but he gave chase.

At some point in the moments that followed - the woman shouted, "'Don't shoot me! I'm pregnant - I'm going to have a baby!'"

"I shot her anyway," Greer said. "The lady didn't run as fast as the man so I shot her in the back twice - she's dead ... but he got away."

Greer told the reporter that he then pulled the woman's body back toward his home. "I shot her twice, she best be dead."

Los Angeles County coroner's officials could not confirm if the woman, who was not immediately identified, was pregnant, pending an autopsy.

Long Beach police said that after questioning Greer, it appeared the woman had been killed after committing a criminal act.

Greer said he had acted in self-defence and had no regrets. In fact, he said, the shooting may have scared off another burglar in the future.

"I've never in my life shot anybody, killed anybody...but when the time comes to defend yourself, you best do something," Greer told KNBC. "Due to the fact his wife or girlfriend is dead, he might think twice before coming back."